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Existence of a ‘structurally stable’ equilibrium for a non-collegial voting rule

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  • Norman Schofield

Abstract

This essay shows that, for any non-collegial voting rule, σ, there exists an integer, s(σ), with this property: if the policy space, W, has dimension no greater than s(σ), then there exists a profile of smooth utilities on W, such that the core for σ at this profile is non-empty and ‘structurally stable’ under sufficiently small perturbation. We also show how we may compute s(σ) for an arbitrary rule. This material is based upon work supported by NSF grant SES-84-18296, to the School of Social Sciences, University of California at Irvine. An early draft was written while the author was Sherman Fairchild Distinguished Scholar at the California Institute of Technology. Thanks are due to Kenneth Shepsle, Dick McKelvey and Gary Cox for helpful comments, to Michael Chwe and Shaun Bowler for research assistance, and to Derek Hearl and Ian Budge for permission to make use of unpublished data. Copyright Martinus Nijhoff Publishers 1986

Suggested Citation

  • Norman Schofield, 1986. "Existence of a ‘structurally stable’ equilibrium for a non-collegial voting rule," Public Choice, Springer, vol. 51(3), pages 267-284, January.
  • Handle: RePEc:kap:pubcho:v:51:y:1986:i:3:p:267-284
    DOI: 10.1007/BF00128877
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    References listed on IDEAS

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    1. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
    2. Norman Schofield, 1983. "Generic Instability of Majority Rule," Review of Economic Studies, Oxford University Press, vol. 50(4), pages 695-705.
    3. McKelvey, Richard D & Schofield, Norman, 1987. "Generalized Symmetry Conditions at a Core Point," Econometrica, Econometric Society, vol. 55(4), pages 923-933, July.
    4. McKelvey, Richard D. & Schofield, Norman, 1986. "Structural instability of the core," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 179-198, June.
    5. Judith Sloss, 1973. "Stable outcomes in majority rule voting games," Public Choice, Springer, vol. 15(1), pages 19-48, June.
    6. Cohen, Linda, 1979. "Cyclic sets in multidimensional voting models," Journal of Economic Theory, Elsevier, vol. 20(1), pages 1-12, February.
    7. Schofield, Norman., "undated". "Classification Theorem for Smooth Social Choice," Working Papers 514, California Institute of Technology, Division of the Humanities and Social Sciences.
    8. repec:cup:apsrev:v:74:y:1980:i:02:p:432-446_16 is not listed on IDEAS
    9. Linda Cohen & Steven Matthews, 1980. "Constrained Plott Equilibria, Directional Equilibria and Global Cycling Sets," Review of Economic Studies, Oxford University Press, vol. 47(5), pages 975-986.
    10. Matthews, Steven A, 1982. "Local Simple Games in Public Choice Mechanisms," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 623-645, October.
    11. Kenneth Shepsle & Barry Weingast, 1981. "Structure-induced equilibrium and legislative choice," Public Choice, Springer, vol. 37(3), pages 503-519, January.
    12. Schofield, Norman, 1980. "Generic properties of simple Bergson-Samuelson welfare functions," Journal of Mathematical Economics, Elsevier, vol. 7(2), pages 175-192, July.
    13. Norman Schofield, 1978. "Instability of Simple Dynamic Games," Review of Economic Studies, Oxford University Press, vol. 45(3), pages 575-594.
    14. Schofield, Norman, 1984. "Social equilibrium and cycles on compact sets," Journal of Economic Theory, Elsevier, vol. 33(1), pages 59-71, June.
    15. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
    16. repec:cup:apsrev:v:78:y:1984:i:02:p:417-434_25 is not listed on IDEAS
    17. Mathew McCubbins & Thomas Schwartz, 1985. "The politics of flatland," Public Choice, Springer, vol. 46(1), pages 45-60, January.
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    Cited by:

    1. Piolatto, Amedeo, 2011. "Plurality versus proportional electoral rule: Which is most representative of voters?," European Journal of Political Economy, Elsevier, vol. 27(2), pages 311-327, June.
    2. Tanner, Thomas Cole, 1994. "The spatial theory of elections: an analysis of voters' predictive dimensions and recovery of the underlying issue space," ISU General Staff Papers 1994010108000018174, Iowa State University, Department of Economics.

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